Social welfare and profit maximization from revealed preferences

Ziwei Ji, Ruta Mehta, Matus Telgarsky

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Consider the seller’s problem of finding optimal prices for her n (divisible) goods when faced with a set of m consumers, given that she can only observe their purchased bundles at posted prices, i.e., revealed preferences. We study both social welfare and profit maximization with revealed preferences. Although social welfare maximization is a seemingly non-convex optimization problem in prices, we show that (i) it can be reduced to a dual convex optimization problem in prices, and (ii) the revealed preferences can be interpreted as supergradients of the concave conjugate of valuation, with which subgradients of the dual function can be computed. We thereby obtain a simple subgradient-based algorithm for strongly concave valuations and convex cost, with query complexity (formula presented), where ϵ is the additive difference between the social welfare induced by our algorithm and the optimum social welfare. We also study social welfare maximization under the online setting, specifically the random permutation model, where consumers arrive one-by-one in a random order. For the case where consumer valuations can be arbitrary continuous functions, we propose a price posting mechanism that achieves an expected social welfare up to an additive factor of (formula Presented) from the maximum social welfare. Finally, for profit maximization (which may be non-convex in simple cases), we give nearly matching upper and lower bounds on the query complexity for separable valuations and cost (i.e., each good can be treated independently).

Original languageEnglish (US)
Title of host publicationWeb and Internet Economics - 14th International Conference, WINE 2018, Proceedings
EditorsTobias Harks, George Christodoulou
PublisherSpringer Verlag
Number of pages18
ISBN (Print)9783030046118
StatePublished - 2018
Event14th International Conference on Web and Internet Economics, WINE 2018 - Oxford, United Kingdom
Duration: Dec 15 2018Dec 17 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11316 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference14th International Conference on Web and Internet Economics, WINE 2018
Country/TerritoryUnited Kingdom

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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